In the paper the optimization problem for subcritical cascade reactor core driven by accelerator is considered. The optimization purpose is to get the maximum reactor power rate for the given effective multiplication factor k_eff, allowable specific energy release and external neutron source intensity. A special feature of cascade reactor cores, especially those with a fast-fast spectrum in theirs sections, is that the neutron distribution function isn't continuously differentiable at the sections boundaries. This fact leads to the non smooth optimization problem.